Oscillatory brain rhythms can bias attention via phase and amplitude changes, which modulate sensory activity, biasing information to be processed or ignored. Alpha band (7-14 Hz) oscillations lateralize with spatial attention and rhythmically inhibit visual activity and awareness through pulses of inhibition. Here we show that human observers' awareness of spatially unattended targets is dependent on both alpha power and alpha phase at target onset. Following a predictive directional cue, alpha oscillations were entrained bilaterally using repetitive visual stimuli. Subsequently, we presented either spatially cued or uncued targets at SOAs either validly or invalidly predicted in time by the entrainers. Temporal validity maximally modulated perceptual performance outside the spatial focus of attention and was associated with both increased alpha power and increased neural entrainment of phase in the hemisphere processing spatially unattended information. The results demonstrate that alpha oscillations represent a pulsating inhibition, which impedes visual processing for unattended space.